Abstract

We describe the design, fabrication, and characterization of a 1-dimensional silicon photonic crystal cavity with a quality factor-to-mode volume ratio greater than 107, which exceeds the highest previous values by an order of magnitude. The maximum of the electric field is outside the silicon in a void formed by a central slot. An extremely small calculated mode volume of 0.0096 (λvac/n)3 is achieved through the abrupt change of the electric field in the slot, despite which a high quality factor of 8.2 × 105 is predicted by simulation. Quality factors up to 1.4 × 105 are measured in actual devices. The observation of pronounced thermo-optic bistability is consistent with the strong confinement of light in these cavities.

© 2013 Optical Society of America

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2013

K. Takeda, T. Sato, A. Shinya, K. Nozaki, W. Kobayashi, H. Taniyama, M. Notomi, K. Hasebe, T. Kakitsuka, S. Matsuo, “Few-fJ/bit data transmissions using directly modulated lambda-scale embedded active region photonic-crystal lasers,” Nat. Photonics 7(7), 569–575 (2013).
[CrossRef]

Y. Takahashi, Y. Inui, M. Chihara, T. Asano, R. Terawaki, S. Noda, “A micrometre-scale Raman silicon laser with a microwatt threshold,” Nature 498(7455), 470–474 (2013).
[CrossRef] [PubMed]

A. H. Safavi-Naeini, S. Gröblacher, J. T. Hill, J. Chan, M. Aspelmeyer, O. Painter, “Squeezed light from a silicon micromechanical resonator,” Nature 500(7461), 185–189 (2013).
[CrossRef] [PubMed]

J. D. Thompson, T. G. Tiecke, N. P. de Leon, J. Feist, A. V. Akimov, M. Gullans, A. S. Zibrov, V. Vuletić, M. D. Lukin, “Coupling a Single Trapped Atom to a Nanoscale Optical Cavity,” Science 340(6137), 1202–1205 (2013).
[CrossRef] [PubMed]

2012

M. Davanço, J. Chan, A. H. Safavi-Naeini, O. Painter, K. Srinivasan, “Slot-mode-coupled optomechanical crystals,” Opt. Express 20(22), 24394–24410 (2012).
[CrossRef] [PubMed]

J. D. Ryckman, S. M. Weiss, “Low mode volume slotted photonic crystal single nanobeam cavity,” Appl. Phys. Lett. 101(7), 071104 (2012).
[CrossRef]

2011

2010

J. Gao, J. F. McMillan, M.-C. Wu, J. Zheng, S. Assefa, C. W. Wong, “Demonstration of an air-slot mode-gap confined photonic crystal slab nanocavity with ultrasmall mode volumes,” Appl. Phys. Lett. 96(5), 051123 (2010).
[CrossRef]

Y. Li, J. Zheng, J. Gao, J. Shu, M. S. Aras, C. W. Wong, “Design of dispersive optomechanical coupling and cooling in ultrahigh-Q/V slot-type photonic crystal cavities,” Opt. Express 18(23), 23844–23856 (2010).
[CrossRef] [PubMed]

M. Galli, D. Gerace, K. Welna, T. F. Krauss, L. O’Faolain, G. Guizzetti, L. C. Andreani, “Low-power continuous-wave generation of visible harmonics in silicon photonic crystal nanocavities,” Opt. Express 18(25), 26613–26624 (2010).
[CrossRef] [PubMed]

A. F. Oskooi, D. Roundy, M. Ibanescu, P. Bermel, J. D. Joannopoulos, S. G. Johnson, “MEEP: A flexible free-software package for electromagnetic simulations by the FDTD method,” Comput. Phys. Commun. 181(3), 687–702 (2010).
[CrossRef]

2009

P. B. Deotare, M. W. McCutcheon, I. W. Frank, M. Khan, M. Lončar, “High quality factor photonic crystal nanobeam cavities,” Appl. Phys. Lett. 94(12), 121106 (2009).
[CrossRef]

A. Di Falco, L. O’Faolain, T. F. Krauss, “Chemical sensing in slotted photonic crystal heterostructure cavities,” Appl. Phys. Lett. 94(6), 063503 (2009).
[CrossRef]

M. Eichenfield, J. Chan, R. M. Camacho, K. J. Vahala, O. Painter, “Optomechanical crystals,” Nature 462(7269), 78–82 (2009).
[CrossRef] [PubMed]

D. A. B. Miller, “Device Requirements for Optical Interconnects to Silicon Chips,” Proc. IEEE 97(7), 1166–1185 (2009).
[CrossRef]

2008

2007

2006

2005

2004

2003

P. Lalanne, J. P. Hugonin, “Bloch-Wave Engineering for High-Q, Small-V Microcavities,” IEEE J. Quantum Electron. 39(11), 1430–1438 (2003).
[CrossRef]

Y. Akahane, T. Asano, B.-S. Song, S. Noda, “High-Q photonic nanocavity in a two-dimensional photonic crystal,” Nature 425(6961), 944–947 (2003).
[CrossRef] [PubMed]

K. J. Vahala, “Optical microcavities,” Nature 424(6950), 839–846 (2003).
[CrossRef] [PubMed]

M. Lončar, A. Scherer, Y. Qiu, “Photonic crystal laser sources for chemical detection,” Appl. Phys. Lett. 82(26), 4648–4650 (2003).
[CrossRef]

2002

J. Vučković, M. Lončar, H. Mabuchi, A. Scherer, “Optimization of the Q Factor in Photonic Crystal Microcavities,” IEEE J. Quantum Electron. 38(7), 850–856 (2002).
[CrossRef]

H. Mabuchi, A. C. Doherty, “Cavity Quantum Electrodynamics: Coherence in Context,” Science 298(5597), 1372–1377 (2002).
[CrossRef] [PubMed]

2001

2000

Y. Xu, Y. Li, R. K. Lee, A. Yariv, “Scattering-theory analysis of waveguide-resonator coupling,” Phys. Rev. E Stat. Phys. Plasmas Fluids Relat. Interdiscip. Topics 62(55 Pt B), 7389–7404 (2000).
[CrossRef] [PubMed]

1999

1997

R. Waldhäusl, B. Schnabel, E.-B. Kley, A. Bräuer, “Efficient focusing polymer waveguide grating couplers,” Electron. Lett. 33(7), 623–624 (1997).
[CrossRef]

1992

V. S. Il’chenko, M. L. Gorodetskii, “Thermal Nonlinear Effects in Optical Whispering Gallery Microresonators,” Laser Phys. 2, 1004–1009 (1992).

1989

V. B. Braginsky, M. L. Gorodetsky, V. S. Ilchenko, “Quality-Factor and Nonlinear Properties of Optical Whsipering-Gallery Modes,” Phys. Lett. A 137(7-8), 393–397 (1989).
[CrossRef]

Akahane, Y.

Y. Akahane, T. Asano, B.-S. Song, S. Noda, “High-Q photonic nanocavity in a two-dimensional photonic crystal,” Nature 425(6961), 944–947 (2003).
[CrossRef] [PubMed]

Akimov, A. V.

J. D. Thompson, T. G. Tiecke, N. P. de Leon, J. Feist, A. V. Akimov, M. Gullans, A. S. Zibrov, V. Vuletić, M. D. Lukin, “Coupling a Single Trapped Atom to a Nanoscale Optical Cavity,” Science 340(6137), 1202–1205 (2013).
[CrossRef] [PubMed]

Almeida, V. R.

Andreani, L. C.

Aras, M. S.

Asano, T.

Y. Takahashi, Y. Inui, M. Chihara, T. Asano, R. Terawaki, S. Noda, “A micrometre-scale Raman silicon laser with a microwatt threshold,” Nature 498(7455), 470–474 (2013).
[CrossRef] [PubMed]

T. Uesugi, B.-S. Song, T. Asano, S. Noda, “Investigation of optical nonlinearities in an ultra-high-Q Si nanocavity in a two-dimensional photonic crystal slab,” Opt. Express 14(1), 377–386 (2006).
[CrossRef] [PubMed]

Y. Akahane, T. Asano, B.-S. Song, S. Noda, “High-Q photonic nanocavity in a two-dimensional photonic crystal,” Nature 425(6961), 944–947 (2003).
[CrossRef] [PubMed]

Aspelmeyer, M.

A. H. Safavi-Naeini, S. Gröblacher, J. T. Hill, J. Chan, M. Aspelmeyer, O. Painter, “Squeezed light from a silicon micromechanical resonator,” Nature 500(7461), 185–189 (2013).
[CrossRef] [PubMed]

Assefa, S.

J. Gao, J. F. McMillan, M.-C. Wu, J. Zheng, S. Assefa, C. W. Wong, “Demonstration of an air-slot mode-gap confined photonic crystal slab nanocavity with ultrasmall mode volumes,” Appl. Phys. Lett. 96(5), 051123 (2010).
[CrossRef]

Atatüre, M.

K. Hennessy, A. Badolato, M. Winger, D. Gerace, M. Atatüre, S. Gulde, S. Fält, E. L. Hu, A. Imamoğlu, “Quantum nature of a strongly coupled single quantum dot-cavity system,” Nature 445(7130), 896–899 (2007).
[CrossRef] [PubMed]

Badolato, A.

K. Hennessy, A. Badolato, M. Winger, D. Gerace, M. Atatüre, S. Gulde, S. Fält, E. L. Hu, A. Imamoğlu, “Quantum nature of a strongly coupled single quantum dot-cavity system,” Nature 445(7130), 896–899 (2007).
[CrossRef] [PubMed]

Barclay, P. E.

Barrios, C. A.

Bermel, P.

A. F. Oskooi, D. Roundy, M. Ibanescu, P. Bermel, J. D. Joannopoulos, S. G. Johnson, “MEEP: A flexible free-software package for electromagnetic simulations by the FDTD method,” Comput. Phys. Commun. 181(3), 687–702 (2010).
[CrossRef]

Bolivar, P.

T. Wahlbrink, T. Mollenhauer, Y. M. Georgiev, W. Henschel, J. K. Efavi, H. D. B. Gottlob, M. C. Lemme, H. Kurz, J. Niehusmann, P. Bolivar, “Highly selective etch process for silicon-on-insulator nano-devices,” Microelectron. Eng. 78-79, 212–217 (2005).
[CrossRef]

Braginsky, V. B.

V. B. Braginsky, M. L. Gorodetsky, V. S. Ilchenko, “Quality-Factor and Nonlinear Properties of Optical Whsipering-Gallery Modes,” Phys. Lett. A 137(7-8), 393–397 (1989).
[CrossRef]

Bräuer, A.

R. Waldhäusl, B. Schnabel, E.-B. Kley, A. Bräuer, “Efficient focusing polymer waveguide grating couplers,” Electron. Lett. 33(7), 623–624 (1997).
[CrossRef]

Camacho, R. M.

M. Eichenfield, J. Chan, R. M. Camacho, K. J. Vahala, O. Painter, “Optomechanical crystals,” Nature 462(7269), 78–82 (2009).
[CrossRef] [PubMed]

Carmon, T.

Chan, J.

A. H. Safavi-Naeini, S. Gröblacher, J. T. Hill, J. Chan, M. Aspelmeyer, O. Painter, “Squeezed light from a silicon micromechanical resonator,” Nature 500(7461), 185–189 (2013).
[CrossRef] [PubMed]

M. Davanço, J. Chan, A. H. Safavi-Naeini, O. Painter, K. Srinivasan, “Slot-mode-coupled optomechanical crystals,” Opt. Express 20(22), 24394–24410 (2012).
[CrossRef] [PubMed]

M. Eichenfield, J. Chan, R. M. Camacho, K. J. Vahala, O. Painter, “Optomechanical crystals,” Nature 462(7269), 78–82 (2009).
[CrossRef] [PubMed]

Chen, L.

J. T. Robinson, C. Manolatou, L. Chen, M. Lipson, “Ultrasmall Mode Volumes in Dielectric Optical Microcavities,” Phys. Rev. Lett. 95(14), 143901 (2005).
[CrossRef] [PubMed]

Chihara, M.

Y. Takahashi, Y. Inui, M. Chihara, T. Asano, R. Terawaki, S. Noda, “A micrometre-scale Raman silicon laser with a microwatt threshold,” Nature 498(7455), 470–474 (2013).
[CrossRef] [PubMed]

Chong, H. M. H.

A. R. M. Zain, M. Gnan, H. M. H. Chong, M. Sorel, R. M. De La Rue, “Tapered Photonic Crystal Microcavities Embedded in Photonic Wire Waveguides With Large Resonance Quality-Factor and High Transmission,” IEEE Photon. Technol. Lett. 20(1), 6–8 (2008).
[CrossRef]

Davanço, M.

De La Rue, R. M.

A. R. M. Zain, M. Gnan, H. M. H. Chong, M. Sorel, R. M. De La Rue, “Tapered Photonic Crystal Microcavities Embedded in Photonic Wire Waveguides With Large Resonance Quality-Factor and High Transmission,” IEEE Photon. Technol. Lett. 20(1), 6–8 (2008).
[CrossRef]

de Leon, N. P.

J. D. Thompson, T. G. Tiecke, N. P. de Leon, J. Feist, A. V. Akimov, M. Gullans, A. S. Zibrov, V. Vuletić, M. D. Lukin, “Coupling a Single Trapped Atom to a Nanoscale Optical Cavity,” Science 340(6137), 1202–1205 (2013).
[CrossRef] [PubMed]

Deotare, P. B.

P. B. Deotare, M. W. McCutcheon, I. W. Frank, M. Khan, M. Lončar, “High quality factor photonic crystal nanobeam cavities,” Appl. Phys. Lett. 94(12), 121106 (2009).
[CrossRef]

Di Falco, A.

A. Di Falco, L. O’Faolain, T. F. Krauss, “Chemical sensing in slotted photonic crystal heterostructure cavities,” Appl. Phys. Lett. 94(6), 063503 (2009).
[CrossRef]

Doherty, A. C.

H. Mabuchi, A. C. Doherty, “Cavity Quantum Electrodynamics: Coherence in Context,” Science 298(5597), 1372–1377 (2002).
[CrossRef] [PubMed]

Efavi, J. K.

T. Wahlbrink, T. Mollenhauer, Y. M. Georgiev, W. Henschel, J. K. Efavi, H. D. B. Gottlob, M. C. Lemme, H. Kurz, J. Niehusmann, P. Bolivar, “Highly selective etch process for silicon-on-insulator nano-devices,” Microelectron. Eng. 78-79, 212–217 (2005).
[CrossRef]

Eichenfield, M.

M. Eichenfield, J. Chan, R. M. Camacho, K. J. Vahala, O. Painter, “Optomechanical crystals,” Nature 462(7269), 78–82 (2009).
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Figures (11)

Fig. 1
Fig. 1

Schematic drawing of the optimized photonic crystal nanobeam cavity with a = 510 nm, w = 550 nm, h = 220 nm, s = 40 nm, and l = 484.5 nm. The hole radius is given by r = 0.365 a . The five holes on either side of the central slot are linearly tapered in spacing and radius to 67% of their nominal value. The color scale indicates the amplitude (blue and red corresponding to opposite signs) of the E y component of the electric field of mode I (see text below) for 2D cross-sections through the center of the cavity taken from a 3D FDTD simulation.

Fig. 2
Fig. 2

Cross-sections through the center of the cavity taken from a 3D FDTD simulation of the optimized nanobeam device showing the in-plane component (arrows) and the total magnitude (color scale) of the electric field of the central portion of mode I. The white lines indicate the boundary between silicon and air. The simulation indicates extreme confinement of the electric field in the slot.

Fig. 3
Fig. 3

Cross-sections through the center of the cavity taken from a 3D FDTD simulation of the optimized nanobeam device showing the in-plane component (arrows) and the total magnitude (color scale) of the electric field of the central portion of mode II. The white lines indicate the boundary between silicon and air. Mode II has a node of zero electric field in the middle of the slot.

Fig. 4
Fig. 4

Scanning electron microscopy image (30° tilt) of a freestanding photonic crystal nanobeam cavity on an SOI wafer with a 40-nm slot. The inset shows a magnified view down the slot (30° tilt). The geometry of the device corresponds to the optimized structure described in section 2. Device Design.

Fig. 5
Fig. 5

Schematic of the experimental apparatus for characterization of the photonic crystal nanobeam cavities.

Fig. 6
Fig. 6

Transmission spectrum of a photonic crystal nanobeam cavity with eight holes on either side of the central slot, where the ordinate indicates the power as detected at the power meter.

Fig. 7
Fig. 7

Normalized spectra showing the resonance peak corresponding to mode I for a series of devices differing only in the total number of holes (including both tapered and non-tapered holes) on either side of the central slot. The irregularity in the peak for the six-hole device is due to interference from reflection between the grating couplers and between the grating couplers and the device structure.

Fig. 8
Fig. 8

Comparison of the measured and simulated behavior of the photonic crystal nanobeam cavity as a function of the number of holes on either side of the central slot. Solid lines with crosses are calculated values from 3D FDTD simulations. Open symbols are measured values from transmission spectra of two different samples with various values for the length l of the slot as noted. (a) Dependence of simulated and measured quality factor Q for modes I and II. (b) Frequencies for modes I and II and mode volume for mode I from simulation. (c) Values of Q / V for mode I inferred from (a) and (b).

Fig. 9
Fig. 9

Normalized transmission spectra of a photonic crystal nanobeam cavity with eight holes on either side of the central slot at two different input intensities, one sufficient to cause dragging of the resonant peak (blue) and one not (red). The spectra were recorded scanning from short wavelength to long wavelength. The power incident on the device after taking into account losses from the grating coupler and coupling waveguide is estimated to be 0.50 μW and 18 μW for the undragged and dragged spectrum, respectively.

Fig. 10
Fig. 10

(a) Distortion of the line shape of resonant peaks as described by Eq. (3). When P i n P b , the peak is Lorentzian (red curve). For higher powers, the peak is distorted toward lower frequency and exhibits hysteretic behavior (vertical dashed lines) depending on the scan direction. (b) Shift of the observed peak maximum for mode I when scanning from short wavelength to long wavelength as a function of the power P o u t leaving the cavity through the output waveguide for a device with eight holes (red) on either side of the central slot and another with nine holes (blue and inset).

Fig. 11
Fig. 11

Thermo-optic shift of the resonance wavelength of a photonic crystal nanobeam device with eight holes (red) on either side of the central slot and another with nine holes (blue).

Equations (5)

Equations on this page are rendered with MathJax. Learn more.

V = ε ( r ) | E ( r ) | 2 d 3 r ε ( r max ) max [ | E ( r max ) | 2 ] ( n ( r max ) λ v a c ) 3
T = 1 4 Q w 2 ( ν ν 0 ν 0 ) 2 + 1 4 Q 2
T = ( Q / Q w ) 2 1 + 4 ( x + P o u t P b ) 2
ν ν 0 ν 0 i Δ n i n i σ i
σ i = i ε i ( r ) | E ( r ) | 2 d 3 r ε ( r ) | E ( r ) | 2 d 3 r

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